Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
r , c = map( int , raw_input().split() );
list1 = [ list( map( int , raw_input().split() ) ) for i in range ( r ) ];
list3 , cc , rr , str1 , str2 = [] , 0 , 0 , 'row ' , 'col ';

if r > c:
     list1 , t , r , str3 , str1 = list( map( list , zip( *list1 ) ) ) , r , c , str1 , str2;
     str2 , c = str3 , t;

list2 = [ [ 0 for j in range ( c ) ] for i in range ( r ) ];    
for i in range ( r ):
         if list1[i][0]:
                 m = min( list1[i] );
                 for j in range ( m ):
                          list3.append('{} {}'.format( str1,i+1 ) )
                 cc += m;
                 for j in range ( c ):
                          list2[i][j] = m;

m = min( list1[0] );
for i in range ( c ):
         if list1[0][i] != m:
                 mm = list1[0][i] - m;
                 for j in range ( mm ):
                          list3.append('{} {}'.format( str2,i+1 ) );
                 cc += mm;
                 for j in range ( r ):
                          list2[j][i] = list2[j][i] + mm;

if list1 == list2:
         print cc;
         for i in list3:
               print i;
else:
         print -1;